During the immune response, the genes coding for antibody variable (V) regions undergo mutation at extremely high rates. This quasi-random process creates and modifies antibody specificity and inevitably introduces deleterious mutations as well. Thus, mutation is a major source of antibody diversity and serves to limit the number of functional antibody forming cells. Many of the essential properties of mutations are known allowing us through mathematical models to quantitate these effects of mutations. Preliminary results show that our model can identify the limits of conditions, such as mutation rate and lymphocyte division time, required to explain data on mutation frequencies, clone size and other manifestations of positive and negative selection. In this way our model will provide testable predictions of the impact of mutation and selection on the immune response. We will extended our current model, then considerably enhance the model by introducing parameters that take into account recently discovered properties of mutation. We will also refine the statistical definition of an antibody combining site and framework to better understand the influence of amino acid substitutions on antibody function. Using our current model, we will investigate the influence of mutation and selection on the distribution of mutations in antibody V regions. We will find the parameters of our clonal proliferation model that best fit mutation distributions in several new large sequence datasets. We will use our model to study why secondary responses are often dominated by clones not found in primary responses. We will investigate the influence of mutation rate, selection schedules, and antigen concentration on clonal expansion and mutation patterns. We will allow mutation to stop after initiation, and allow antigen concentration to diminish in response to proliferating cells. Mutation induces diversity, an important property of antibody responses which needs to be better understood. Therefore, we will assess the clonal diversity of simulated immune responses and find model parameters to match that of observed clones. To permit this assessment, we will simulate exact (AGCT) sequences and keep track of each mutation. We will assess the development of diversity during clonal expansion and use Shannon information to quantify it. We will develop methods of imputation of genealogic trees and use algorithms to compare model and laboratory- generated trees in order to optimize model parameters. We will adjust the model to match computer-generated mutant sequences to mutant V genes isolated from NP-specific germinal centers at various time points. This will determine the selective value of key mutations required to account for their prevalence in antigen-selected populations of B cells. Our results should provide needed means for analysis of accumulated data on somatic mutation and provide us with a detailed view of this process. They should also suggest future experimental directions. Finally, they could provide a theoretical basis for design of immunization protocols to maximize diversity and for understanding the role of somatic mutation in autoimmunity and B cell lymphomas.